Geodesic
Almost disjoint families and property (a)
Fundamenta Mathematicae, Tome 158 (1998) no. 3, pp. 229-240 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We consider the question: when does a Ψ-space satisfy property (a)? We show that if $|A| \got p$ then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality $\got p$ which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).
DOI : 10.4064/fm-158-3-229-240
Keywords: property (a), density, extent, almost disjoint families, Ψ-space, CH, GCH, Martin's Axiom, $\got p = \got c$, Cohen forcing, Q-set, weakly inaccessible cardinal.

Paul J. Szeptycki 1 ; Jerry E. Vaughan 1

1 
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Paul J. Szeptycki; Jerry E. Vaughan. Almost disjoint families and property (a). Fundamenta Mathematicae, Tome 158 (1998) no. 3, pp. 229-240. doi: 10.4064/fm-158-3-229-240

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